Apparatus and Method for Generating Identification Key

ABSTRACT

Provided is a PUF by which an identification key is generated according to a random event caused by a semiconductor process variation. The PUF can provide the identification key as a result of electrical differences among elements. According to one embodiment, the PUF can accumulate the electrical differences and/or instantaneous values without generating the identification key by using the instantaneous values caused by the electrical differences. The accumulation may be the accumulation of a discrete iteration and the result thereof. However, according to another embodiment, the accumulation may be a continuation of the accumulation result during time intervals.

TECHNICAL FIELD

Example embodiments relate to a method and apparatus for generating anidentification key, and more particularly, to a method by which aphysically unclonable function (PUF) increases a reliability of anidentification key.

BACKGROUND ART

A physically unclonable function (PUF) may provide an unpredictabledigital value. Although a manufacturing process is precisely designedand PUFs are manufactured in the same process, the PUFs may providedifferent digital values. The PUF may also be referred to as physicalone-way function practically impossible to be duplicated (POWF).

Such an unduplicable characteristic of the PUF may be applied togenerate an identifier of a device for security and/or authentication.For example, the PUF may be used to provide a unique key to distinguishdevices from one another.

Korean Patent No. 10-1139630 (hereinafter, referred to as patent '630)and Korean Patent No. 10-0926214 (hereinafter, referred to as patent'214) disclose methods of implementing a PUF. The patent '630 disclosesa method of stochastically determining whether to generate inter-layercontact or a via between conductive layers of a semiconductor by using asemiconductor process variation. The patent '214 discloses a method ofimplementing a PUF based on a fact that current driving capabilities orthreshold voltages of two identically designed and manufacturedelectrical elements are not completely equal due to the semiconductorprocess variation.

DISCLOSURE OF INVENTION Technical Solutions

According to an aspect, there is provided an apparatus for generating anidentification key, the apparatus including: a generator configured toprovide a random event based on a semiconductor process variation, theevent being associated with an electrical property difference; anaccumulator configured to perform an accumulation on the random event toprovide a cumulative result value; and a reader configured to determinethe cumulative result value to be a binary value corresponding to one of0 and 1 based on a predetermined reference and provide an identificationkey corresponding to the generator. According to an example embodiment,the electrical property values or the differences between the electricalproperty values may be accumulated. According to another exampleembodiment, it is possible to accumulate digital values, for example,binary values generated using a predetermined method based on events. Inthis example, the binary values of the events may not be provided as anidentification key directly. Instead, results corresponding to eventsmay be accumulated such that a result is provided based on a cumulativevalue. The accumulation may be a discrete iteration and an accumulationof discrete iteration results. Also, the accumulation may indicate anaccumulation of results performed analogously for a predetermined periodof time.

The random event may include an event that, between two identicallydesigned and manufactured elements, a first element has a greaterelectrical property value than that of a second element.

Each of the first element and the second element may include a capacitorand the electrical property value may include a capacitance. Theaccumulator may generate a quantity of charge proportional to adifference between a first capacitance corresponding to the firstelement and a second capacitance corresponding to the second element.The accumulator may include an integrator configured to accumulate thequantity of charge into an output. The integrator may iterate anaccumulation of the quantity of charge into the output a plurality oftimes until a predetermined condition is satisfied. Also, the integratormay provide a value of the output obtained by iterating the accumulationthe plurality of times. According to an example embodiment, theintegrator may be a fully differential integrator. According to anotherexample embodiment, the integrator may be a one-ended integrator.

The predetermined condition may include the value of the output beinggreater than or equal to a threshold. The predetermined condition mayinclude an iteration being performed k times determined in advance, kbeing a natural number.

Each of the first element and the second element may include a resistorand the electrical property value includes a resistance value. Theaccumulator may include an integrator configured to accumulate a currentproportional to a difference in resistance value into an output. Theaccumulator may be configured to perform a current integration byaccumulating, into an output, a current proportional to a differencebetween a first resistance value corresponding to the first element anda second resistance value corresponding to the second element until apredetermined condition is satisfied, and provide a value of the outputin a case in which the predetermined condition is satisfied.

The predetermined condition may include the value of the output beinggreater than or equal to a threshold but not limited thereto. Thepredetermined condition may include the current integration beingperformed for a predetermined period of time.

According to another aspect, there is also provided an apparatus forgenerating an identification key, the apparatus including: a generatorincluding a first element having an electrical property value differingfrom electrical property values of elements designed identically to thefirst element, based on a semiconductor process variation, wherein anelectrical value is output based on whether the electrical propertyvalue is greater than a reference value; an accumulator configured toperform an accumulation on the electrical value and provide a cumulativeresult value; and a reader configured to provide an identification keycorresponding to the generator based on the cumulative result value.

The electrical property value may include a resistance value. Theaccumulator may include an integrator configured to accumulate a currentcorresponding to the resistance value into an output. The integrator maybe configured to perform a current integration by accumulating, into anoutput, a current proportional to a difference between the firstresistance value and the reference value until a predetermined conditionis satisfied, and provide a value of the output in a case in which thepredetermined condition is satisfied. The predetermined condition mayinclude the current integration being performed for a predeterminedperiod of time.

According to still another aspect, there is also provided a method ofoperating an identification key generating apparatus to generate anidentification key, the method including: generating, by a generator, arandom event based on a semiconductor process variation; accumulating aresult of the random event using a predetermined scheme and providing acumulative result value obtained by accumulating a result value of therandom event; and reading an identification key corresponding to theidentification key generating apparatus using the cumulative resultvalue. The random event may include an event that, between twoidentically designed and manufactured elements, a first element has agreater electrical property value than that of a second element.

Each of the first element and the second element may include a capacitorand the electrical property value may include a capacitance. Theaccumulating may include generating a quantity of charge proportional toa difference between a first capacitance corresponding to the firstelement and a second capacitance corresponding to the second element anditerating an accumulation of the quantity of charge into an output aplurality of times until a predetermined condition is satisfied.

Each of the first element and the second element may include a resistorand the electrical property value includes a resistance value. Theaccumulating may include performing a current integration byaccumulating, into an output, a current proportional to a differencebetween a first resistance value corresponding to the first element anda second resistance value corresponding to the second element until apredetermined condition is satisfied. The predetermined condition mayinclude the current integration being performed for a predeterminedperiod of time. Also, the predetermined condition may include theaccumulating repetitively performed until the value of the output isgreater than or equal to a threshold.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram illustrating an identification key generatingapparatus according to an example embodiment.

FIG. 2 is a circuit diagram illustrating an example of implementing anidentification key generating apparatus according to an exampleembodiment.

FIGS. 3 through 5B are diagrams illustrating a process of providing anidentification key by accumulating electrical property value differencesin the example embodiment of FIG. 2.

FIG. 6 is a circuit diagram illustrating an example of implementing anidentification key generating apparatus according to an exampleembodiment.

FIGS. 7A through 9 are diagrams illustrating a process of providing anidentification key by accumulating electrical property value differencesin the example embodiment of FIG. 6.

FIG. 10 is a circuit diagram illustrating an example of implementing anidentification key generating apparatus according to an exampleembodiment.

FIGS. 11A and 11B are diagrams illustrating a process of providing anidentification key by accumulating electrical property value differencesin the example embodiment of FIG. 10.

FIG. 12 is a flowchart illustrating a method of operating anidentification key generating apparatus according to an exampleembodiment.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, example embodiments will be described in detail withreference to the accompanying drawings. It should be understood,however, that there is no intent to limit this disclosure to theparticular example embodiments disclosed. Like numbers refer to likeelements throughout the description of the figures.

Terminologies used herein are defined to appropriately describe theexample embodiments of the present disclosure and thus may be changeddepending on a user, the intent of an operator, or a custom.Accordingly, the terminologies must be defined based on the followingoverall description of this specification.

It will be further understood that terms, such as those defined incommonly used dictionaries, should be interpreted as having a meaningthat is consistent with their meaning in the context of the relevant artand will not be interpreted in an idealized or overly formal senseunless expressly so defined herein.

FIG. 1 is a block diagram illustrating an apparatus 100 for generatingidentification key according to an example embodiment. The apparatus 100may include a generator 101 configured to provide a random event basedon a semiconductor process variation. Here, the event may be associatedwith an electrical property difference. An electrical property may be,but not limited to, a resistance value of a resistor corresponding to apassive element, a capacitance of a capacitor, a current drivecapability of an active device such as a transistor, and a thresholdvoltage. The generator 101 may intrinsically provide the electricalproperty or an electrical property difference value between elements. Adifference in electrical property value may occur due to thesemiconductor process variation.

The difference in electrical property value may correspond to asignificantly small value. Thus, the electrical property value may bechanged by various environmental factors such as thermal noise, aging ofan element, a disturbance such as an electromagnetic wave. When a uniqueidentification key is generated by a value of a physically unclonablefunction (PUF) using the electrical property value or the electricalproperty difference value between elements, a change due to theaforementioned environmental factors may cause an undesirable result.Hereinafter, the identification key may include a digital value such asa secret key for authentication, a personal key, a unique ID of adevice, and the like. When the identification key is changed, it may bea challenge for a reliability of a PUF and a security apparatusincluding the PUF. Thus, a time invariance in which the identificationvalue corresponding to the PUF value does not change over time may needto be ensured.

The apparatus 100 may include an accumulator 102 that provides acumulative result value by accumulating events provided by the generator101. According to an example embodiment, the electrical property valuesor the differences between the electrical property values may beaccumulated. Such accumulation may indicate that analog electricalproperties, for example, a quantity of charge, current, and a potentialdifference are integrated in an electric circuit.

However, the integration performed on the quantity of charge and/or thecurrent in the electrical circuit is merely an example. According toanother example embodiment, it is possible to accumulate digital values,for example, binary values generated using a predetermined method basedon events. In this example, the binary values of the events may not beprovided as an identification key directly. Instead, resultscorresponding to events may be accumulated such that a result isprovided based on a cumulative value. The accumulation may be a discreteiteration and an accumulation of discrete iteration results. However,the accumulation may indicate not only the discrete iteration and theaccumulation of discrete iteration results, but also an accumulation ofresults performed analogously for a predetermined period of time.

A reader 103 may determine the cumulative result value to be a binaryvalue corresponding to one of 0 and 1 based on a predetermined referenceand provide the determined binary value as an identification keycorresponding to the generator 101. In a related art, a general PUF mayread an event intrinsically provided by the generator 101 and use theevent as a PUF value. In the present disclosure, the apparatus 100 mayaccumulate, using the accumulator 102, electric properties or propertydifference values generated by the generator 101, and allow the reader103 to provide an identification key using a cumulative result. Examplesof the generator 101 and the accumulator 102 will be further describedwith reference to the following drawings.

FIG. 2 is a circuit diagram illustrating an example of implementing anidentification key generating apparatus according to an exampleembodiment. An event may include, for example, an event that, betweentwo identically designed and manufactured elements, a first element hasa greater electrical property value than that of a second element. Eachof the first element and the second element may include a capacitor andthe electrical property value may include a capacitance.

Referring to FIG. 2, a generator 210 may include a capacitor Ca that isa first element and a capacitor Cb that is a second element. When avoltage is applied to the generator 210, a quantity of chargeproportional to a difference between a first capacitance of thecapacitor Ca and a second capacitance of the capacitor Cb may beaccumulated in an accumulator 220. A reader 230 may provide a PUF value,for example, binary value based on am accumulated result value using acomparator. An operation method will be further described with referenceto the following drawings, starting from FIG. 3

FIGS. 3 through 5B are diagrams illustrating a process of providing anidentification key by accumulating differences in electrical propertyvalue in the example embodiment of FIG. 2. In the example of FIG. 2, theaccumulator 220 may include a fully differential integrator. A circuitillustrated in the drawing is merely an example of the fullydifferential integrator and thus, integrators having various structuresare also applicable thereto.

Referring to FIG. 3, when a reset switch 224 is closed, for example,switched on in response to a connection, voltages of VINP, VINN, VOUTP,VOUTN, and VREF may have the same value. In this example, a quantity ofcharge remaining in a capacitor CF may be totally discharged. A processin which the reset switch 224 is closed may be understood as a processin which a circuit is initialized before an accumulation is performed.

Referring to FIG. 4A, the reset switch 224 may be open, for example,switched off. In this example, voltages of VINP, VINN, and VREF may havethe same value. Also, in the capacitor CF, a quantity of chargeproportional to a capacitance difference between the capacitor Ca thatis a first element and the capacitor Cb that is a second element may beaccumulated. The quantity of charge accumulated in the capacitor CF maybe represented by voltage values of VOUTP and VOUTN corresponding tooutput voltages.

Referring to FIGS. 4A and 4B, when ΔVEX that is a voltage difference ofVEX is applied to the first element Ca, a node in a direction in whichΔVEX of the first element Ca is applied may be charged with Qa, which isa positive charge quantity corresponding to a result of multiplicationof ΔVEX and a first capacitance of the first element Ca. Sincetwo-directional nodes of the first element Ca are to be charged with thesame quantity of charge having different polarities, a VINP-directionalnode may be charged with Qa, which is a negative charge quantity. InFIG. 4B, when −ΔVEX that is a voltage difference of VEXB is applied tothe second element Cb, a VEXB-directional node of the second element Cbmay be charged with Qb, which is a negative charge quantitycorresponding to a result of multiplication of ΔVEX and a secondcapacitance of the second element Cb. Since two-directional nodes of thesecond element Cb are to be charged with the same quantity of chargehaving different polarities, a VINP-directional node may be charged withQb, which is a positive quantity charge. Through this, −ΔQ that is atotal change in the quantity of charge in the VINP-directional node maycorrespond to a value of −(Qa−Qb). That is, a value of ΔQ may have amagnitude of “ΔVEX·(Ca−Cb)” corresponding to a value obtained bymultiplying ΔVEX by a magnitude obtained by subtracting the secondcapacitance of the second element Cb from the first capacitance of thefirst element Ca. In this example, to maintain a total charge of VINP ata value of 0, a total quantity of charge in two directional nodes of thecapacitor CF may be changed by +ΔQ having a value of “ΔVEX·(Ca−Cb).”

+^(Δ)Q may cause different operations of output voltages in acommon-mode and a differential mode based on operations of adifferential amplifier. A common-mode change may not affect adifferential operation. In terms of a differential-mode change, valuesof VOUTP and VOUTN corresponding to the output voltages may be changedto satisfy a quantity of charge corresponding to the change. VOUTP maybe changed to a value obtained by dividing a value of a half of +^(Δ)Qby a magnitude of a capacitance of the capacitor CF. VOUTN may bechanged to a value obtained by dividing a value of a half of −^(Δ)Q bythe magnitude of the capacitance of the capacitor CF. The changed valuesof the output voltages may correspond to outputs of the accumulator 220in the examples of FIGS. 2, 3, and 4A.

Referring to FIGS. 5A and 5B, when −^(Δ)VEX that is a voltage differenceof VEX is applied to the first element Ca, a VEX-directional node may becharged with Qa, which is a negative charge quantity corresponding to aresult of multiplication of ΔVEX and a first capacitance of the firstelement Ca. Since two-directional nodes of the first element Ca are tobe charged with the same quantity of charge having different polarities,a VINP-directional node may be charged with Qa, which is a positivecharge quantity.

As described with reference to FIG. 4B, when a voltage difference ofVEXB is applied by ΔVEX, a VEXB-directional node of the second elementCb may be charged with Qb, which is a positive charge quantitycorresponding to a result of multiplication of ΔVEX and a secondcapacitance of the second element Cb. Since two-directional nodes of thesecond element Cb are to be charged with the same quantity of chargehaving different polarities, a VINP-directional node may be charged withQb, which is a negative quantity charge. Through this, ΔQ that is atotal change in the quantity of charge in the VINP-directional node maycorrespond to a value of “Qa−Qb”. That is, a value of ΔQ may have amagnitude of “ΔVEX·(Ca−Cb)” corresponding to a value obtained bymultiplying ΔVEX by a magnitude obtained by subtracting the secondcapacitance of the second element Cb from the first capacitance of thefirst element Ca.

To maintain a total charge of VINP at a value of 0, a total quantity ofcharge in two directional nodes of the capacitor CF may be changed by−ΔQ having a value of “ΔVEX·(Ca−Cb).”−ΔQ may cause different operationsof output voltages in a common-mode and a differential mode based onoperations of a differential amplifier. A common-mode change may notaffect a differential operation.

In terms of a differential-mode change, values of VOUTP and VOUTNcorresponding to the output voltages may be changed to satisfy aquantity of charge corresponding to the change. VOUTP may be changed toa value obtained by dividing a value of a half of +ΔQ by a magnitude ofa capacitance of the capacitor CF. VOUTN may be changed to a valueobtained by dividing a value of a half of −ΔQ by the magnitude of thecapacitance of the capacitor CF. The changed values of the outputvoltages may correspond to outputs of the accumulator 220 in theexamples of FIGS. 2, 3, and 5A.

Although an integrator is described as a fully differential integratorin the above examples, a one-ended integrator is also applicablethereto. FIG. 6 is a circuit diagram illustrating an example ofimplementing an identification key generating apparatus according to anexample embodiment. In the present example, an integrator may be theone-ended integrator.

Similar to the above description, in a generator 310, electric propertyvalues may be accumulated due to a capacitance difference between acapacitor Ca and a capacitor Cb. An accumulator 320 may include switches321 and 322 configured to select a phase to allow an output to increaseor decrease in one direction. Also, the accumulator 320 may include areset switch 324 configured to initialize a circuit by fully discharginga quantity of charge remaining in a capacitor CF when the reset switch324 is switched on. A structure of the accumulator 320 illustrated inthe drawing is merely an example of implementing a single-endedintegrator and single-ended integrator in other structures are alsoapplicable thereto. When the accumulator 320 accumulates a quantity ofcharge corresponding to the capacitance difference between the capacitorCa and the capacitor Cb as a result value, a reader 330 may compare acumulative result to VREF to read an identification key.

FIGS. 7A through 9 are diagrams illustrating a process of providing anidentification key by accumulating electrical property value differencesin the example embodiment of FIG. 6. Referring to FIGS. 7A and 7B, aswitch sw1 321 may be in an on state, a switch sw2 322 may be in an offstate, and a reset switch sw3 324 may be in the off state. Although aquantity of charge to be charged in each of the first element Ca and thesecond element Cb is changed in response to a change in voltage of eachof VEX and VEXB corresponding to voltages, because the switch sw2 322 isin the off state, the changes in voltage of VEX and VEXB may betransferred to Vref via the switch sw1 321 instead of an amplifier. Inthis example, a change in voltage applied to each of VEX and VEXB may bea voltage difference of +ΔVEX and −ΔVEXB at a point in time of φ1(Phase 1) as illustrated in FIG. 7B. A cumulative quantity of charge inthe capacitor CF may be fully discharged using the reset switch 324.

Referring to FIGS. 8A and 8B, the switch sw1 321 may be in the offstate, the switch sw2 322 may be in the on state, and the reset switchsw3 324 may be in the off state. In response to a change in voltage ofeach of VEX and VEXB corresponding to voltages, a quantity of charge tobe charged in each of the first element Ca and the second element Cb maybe changed. In this example, it is assumed that changes in thequantities of charge are magnitudes of Qa and Qb. To maintain a totalquantity of charge in a node of VINP at a value of 0, changes inquantities of charge having the same magnitude as a value obtained bysubtracting a quantity of charge Qb in the second element Cb from aquantity of charge Qa in the first element Ca and opposite polaritiesmay occur in the capacitor CF.

Here, +ΔQ may be the value obtained by subtracting a quantity of chargeQb in the second element Cb from a quantity of charge Qa in the firstelement Ca. In this example, a node in a direction in which the node isconnected to VINN of the capacitor CF may be changed with a quantity ofchange corresponding to a magnitude of −ΔQ, and a VOUT-directional nodeopposite to the node may be charged with a quantity of chargecorresponding to a magnitude of +ΔQ. In response to the quantity ofcharge being charged in the VOUT-directional node by +ΔQ, a voltagechange corresponding to a value obtained by multiplying VEX which is avoltage by a value obtained by dividing a difference between the firstcapacitance of the first element Ca and the second capacitance of thesecond element Cb by a magnitude of a capacitance of the capacitor CFmay occur in a node of VOUT. Such values of changes in output voltagesmay correspond to outputs of the accumulator 320 in the examples ofFIGS. 6, 7A, and 8A. In this instance, a change in voltage applied toeach of VEX and VEXB may be a voltage difference of +ΔVEX and −ΔVEXBcorresponding to a point in time of φ2 (Phase 2) as illustrated in FIG.7B.

Referring to FIG. 9, in φ1 (Phase 1), an accumulation may not beperformed in the accumulator 320 of the identification key generatingapparatus. Also, only in φ2 (Phase 2), the accumulation may berepetitively performed in the accumulator 320 of the identification keygenerating apparatus. In this example, a magnitude by which theaccumulation is performed may be changed based on a magnitude of (Ca−Cb)corresponding to a difference between the first capacitance of the firstelement Ca and the second capacitance of the second element Cb, andcorrespond to a size of a process variation.

Such accumulation of a quantity of charge may be repetitively and/orconsistently performed while a predetermined condition is satisfied. Inan example, the predetermined condition may include a cumulative outputvalue being greater than or equal to a threshold. The threshold may besufficient to ensure a PUF value remaining the same irrespective of anexternal environmental factor such as noise or an internal factor suchas an aging of an element. In another example, the predeterminedcondition may be an iteration performed k times, k being a naturalnumber. An iteration count k may be determined based on a process and/ora predetermined element or an element specification. Also, an optimalvalue may be determined through the iteration performed by those skilledin the art.

FIG. 10 is a circuit diagram illustrating an example of implementing anidentification key generating apparatus according to an exampleembodiment. In the present example, a first element and a second elementof which electrical properties are compared to each other may beresistors. The resistors may include the resistors RA and RB which aredesigned to have the same size in a generator 410 and have resistancevalues not to be completely equal due to process variations. Thecompared electrical property values may be the resistance values. Anaccumulator 420 may include an integrator configured to accumulatecurrent proportional to a difference between the resistance values intoan output. The integrator may perform a current integration byaccumulating current proportional to a difference between a firstresistance value of the resistor RA and a second resistance value of theresistor RB into an output. Also, the integrator may consistentlyperform the current integration until a predetermined condition issatisfied, and then provide an output value obtained therefrom. A reader430 may provide a PUF value, for example, a binary value based on acumulative result value using a comparator.

In an example, the predetermined condition may include a cumulativeoutput value being greater than or equal to a threshold. The thresholdmay be sufficient to ensure a PUF value remaining the same irrespectiveof an external environmental factor such as noise or an internal factorsuch as an aging of an element. In another example, the predeterminedcondition may be the current integration performed for a predeterminedperiod of time. The period of time may be determined based on a processand/or a predetermined element or an element specification. Also, anoptimal value may be determined through the iteration performed by thoseskilled in the art.

FIGS. 11A and 11B are diagrams illustrating a process of providing anidentification key by accumulating electrical property value differencesin the example embodiment of FIG. 10. When a reset switch 424 isswitched on, a quantity of charge remaining in the capacitor CF may befully discharged such that a circuit is initialized. Referring to FIGS.11A and 11B, a current flowing in the capacitor CF of the accumulator420 may be proportional to a value obtained by differentiating a voltagedifference between both ends of the capacitor CF with respect to time.In this example, a constant current flowing in the capacitor CF mayindicate that the value obtained by differentiating the voltagedifference between the both ends of the capacitor CF is a constantvalue.

When the current generated proportionally to magnitudes of the resistorsRA and RB of the generator 410 flows in the capacitor CF of theaccumulator 420, the value obtained by differentiating the voltagedifference between the both ends of the capacitor CF may change. In theaccumulator 420, because an input voltage of an amplifier maintains avalue of VREF that is a voltage through an operation of a negativefeedback, the value obtained by differentiating the voltage differencebetween the both ends of the capacitor CF may generate VOUTP and VOUTNcorresponding to output voltages. Changes in an output voltage value maybe continuously accumulated by the lapse of time. Such values of thechanges in the output voltages may correspond to outputs of theaccumulator 420 in the example of FIGS. 10 and 11A. FIG. 11B illustratesvalues of VOUTP and VOUTN corresponding to the output voltages of theaccumulator 420, the values which are accumulated based on an operationof the identification generating apparatus of FIG. 11A.

In FIG. 11A, the current flowing in the capacitor CF may not affectVOUTP and VOUTN corresponding to output voltages in a common-mode whilea current difference occurs in a differential-mode, which may lead tochanges in VOUTP and VOUTN corresponding to the output voltages. In FIG.11B, gradients of changes in VOUTP and VOUTN may correspond to amagnitude obtained by dividing, by a capacitance value of the capacitorCF, a half of a current difference value based on a resistancedifference occurring due to a process variation of each of the resistorsRA and RB of FIG. 10.

FIG. 12 is a flowchart illustrating a method of operating anidentification key generating apparatus according to an exampleembodiment. According to an example embodiment, a method of generatingan identification key using an identification key generating apparatusmay be provided. The method may include: operation 501 in which agenerator generates a random event based on a semiconductor processvariation; operation 502 of performing an accumulation on a result ofthe event using a predetermined scheme and providing a cumulative resultvalue obtained through the accumulation; and operation 503 of reading anidentification key corresponding to the identification key generatingapparatus using the cumulative result value.

In operation 501, electrical properties of elements or electricalproperty differences between elements may occur based on thesemiconductor process variation. For example, between two identicallydesigned and manufactured elements, a first element may have a greaterelectrical property value than that of a second element. For example,each of the first element and the second element includes a capacitorand the electrical property value includes a capacitance. In operation502, the electrical properties or the electrical property differencesmay be accumulated as a result value. Such accumulation may include aprocess of generating a quantity of charge proportional to a differencebetween a first capacitance corresponding to the first element and asecond capacitance corresponding to the second element and a process ofrepetitively accumulating the quantity of charge into an output aplurality of times until a predetermined condition is satisfied.

In an example, each of the first element and the second element mayinclude a resistance and the electrical property value may include aresistance value. In this example, a process of repetitively perform acurrent integration by accumulating currents proportional to adifference between a first resistance value corresponding to the firstelement and a second resistance value corresponding to the secondelement into an output until a predetermined condition is satisfied maybe performed in operation 502. Here, the predetermined condition may beto perform the current integration for a predetermined period of time.Depending on an example, the condition may include the accumulationcontinuously performed until a value of the output is greater than orequal to a threshold.

The units described herein may be implemented using hardware componentsand software components. For example, the hardware components mayinclude microphones, amplifiers, band-pass filters, audio to digitalconvertors, and processing devices. A processing device may beimplemented using one or more general-purpose or special purposecomputers, such as, for example, a processor, a controller and anarithmetic logic unit, a digital signal processor, a microcomputer, afield programmable array, a programmable logic unit, a microprocessor orany other device capable of responding to and executing instructions ina defined manner. The processing device may run an operating system (OS)and one or more software applications that run on the OS. The processingdevice also may access, store, manipulate, process, and create data inresponse to execution of the software. For purpose of simplicity, thedescription of a processing device is used as singular; however, oneskilled in the art will appreciated that a processing device may includemultiple processing elements and multiple types of processing elements.For example, a processing device may include multiple processors or aprocessor and a controller. In addition, different processingconfigurations are possible, such a parallel processors.

The software may include a computer program, a piece of code, aninstruction, or some combination thereof, for independently orcollectively instructing or configuring the processing device to operateas desired. Software and data may be embodied permanently or temporarilyin any type of machine, component, physical or virtual equipment,computer storage medium or device, or in a propagated signal wavecapable of providing instructions or data to or being interpreted by theprocessing device. The software also may be distributed over networkcoupled computer systems so that the software is stored and executed ina distributed fashion. In particular, the software and data may bestored by one or more computer readable recording mediums.

The methods according to the above-described embodiments may berecorded, stored, or fixed in one or more non-transitorycomputer-readable media that includes program instructions to beimplemented by a computer to cause a processor to execute or perform theprogram instructions. The media may also include, alone or incombination with the program instructions, data files, data structures,and the like. The program instructions recorded on the media may bethose specially designed and constructed, or they may be of the kindwell-known and available to those having skill in the computer softwarearts. Examples of non-transitory computer-readable media includemagnetic media such as hard disks, floppy disks, and magnetic tape;optical media such as CD ROM discs and DVDs; magneto-optical media suchas optical discs; and hardware devices that are specially configured tostore and perform program instructions, such as read-only memory (ROM),random access memory (RAM), flash memory, and the like. Examples ofprogram instructions include both machine code, such as produced by acompiler, and files containing higher level code that may be executed bythe computer using an interpreter. The described hardware devices may beconfigured to act as one or more software modules in order to performthe operations and methods described above, or vice versa.

A number of example embodiments have been described above. Nevertheless,it should be understood that various modifications may be made to theseexample embodiments. For example, suitable results may be achieved ifthe described techniques are performed in a different order and/or ifcomponents in a described system, architecture, device, or circuit arecombined in a different manner and/or replaced or supplemented by othercomponents or their equivalents. Accordingly, other implementations arewithin the scope of the following claims.

1. An apparatus for generating an identification key, the apparatuscomprising: a generator configured to provide a random event based on asemiconductor process variation, the event being associated with anelectrical property difference; an accumulator configured to perform anaccumulation on the random event to provide a cumulative result value;and a reader configured to determine the cumulative result value to be abinary value corresponding to one of 0 and 1 based on a predeterminedreference and provide an identification key corresponding to thegenerator.
 2. The apparatus of claim 1, wherein the random eventincludes an event that, between two identically designed andmanufactured elements, a first element has a greater electrical propertyvalue than that of a second element.
 3. The apparatus of claim 2,wherein each of the first element and the second element includes acapacitor and the electrical property value includes a capacitance. 4.The apparatus of claim 3, wherein the accumulator comprises: anintegrator configured to generate a quantity of charge proportional to adifference between a first capacitance corresponding to the firstelement and a second capacitance corresponding to the second element,iterate an accumulation of the quantity of charge into an output aplurality of times until a predetermined condition is satisfied, andprovide a value of the output obtained by iterating the accumulation theplurality of times.
 5. The apparatus of claim 4, wherein thepredetermined condition includes the value of the output being greaterthan or equal to a threshold.
 6. The apparatus of claim 4, wherein thepredetermined condition includes an iteration being performed k timesdetermined in advance, k being a natural number.
 7. The apparatus ofclaim 2, wherein each of the first element and the second elementincludes a resistor and the electrical property value includes aresistance value.
 8. The apparatus of claim 7, wherein the accumulatorcomprises: an integrator configured to perform a current integration byaccumulating, into an output, a current proportional to a differencebetween a first resistance value corresponding to the first element anda second resistance value corresponding to the second element until apredetermined condition is satisfied, and provide a value of the outputin a case in which the predetermined condition is satisfied.
 9. Theapparatus of claim 8, wherein the predetermined condition includes thevalue of the output being greater than or equal to a threshold.
 10. Theapparatus of claim 8, wherein the predetermined condition includes thecurrent integration being performed for a predetermined period of time.11. An apparatus for generating an identification key, the apparatuscomprising: a generator including a first element having an electricalproperty value differing from electrical property values of elementsdesigned identically to the first element, based on a semiconductorprocess variation, wherein an electrical value is output based onwhether the electrical property value is greater than a reference value;an accumulator configured to perform an accumulation on the electricalvalue and provide a cumulative result value; and a reader configured toprovide an identification key corresponding to the generator based onthe cumulative result value.
 12. The apparatus of claim 11, wherein theelectrical property value includes a resistance value.
 13. The apparatusof claim 12, wherein the accumulator comprises: an integrator configuredto perform a voltage distribution of a power source voltage based on aratio between a first resistance value corresponding to the firstelement and the reference value, perform a current integration byaccumulating, into an output, a current proportional to a differencebetween the first resistance value and the reference value until apredetermined condition is satisfied, and provide a value of the outputin a case in which the predetermined condition is satisfied.
 14. Theapparatus of claim 13, wherein the predetermined condition includes thecurrent integration being performed for a predetermined period of time.15. A method of operating an identification key generating apparatus togenerate an identification key, the method comprising: generating, by agenerator, a random event based on a semiconductor process variation;accumulating a result of the random event using a predetermined schemeand providing a cumulative result value obtained by accumulating aresult value of the random event; and reading an identification keycorresponding to the identification key generating apparatus using thecumulative result value.
 16. The method of claim 15, wherein the randomevent includes an event that, between two identically designed andmanufactured elements, a first element has a greater electrical propertyvalue than that of a second element.
 17. The method of claim 16, whereineach of the first element and the second element includes a capacitorand the electrical property value includes a capacitance.
 18. The methodof claim 17, wherein the accumulating comprises generating a quantity ofcharge proportional to a difference between a first capacitancecorresponding to the first element and a second capacitancecorresponding to the second element and iterating an accumulation of thequantity of charge into an output a plurality of times until apredetermined condition is satisfied.